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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Quadratic Equation

BITSAT 2011 · Mathematics · Quadratic Equation

If ( α, β ) are the roots of the equation ( ax^ 2+ bx+c= 0), then...

If (α,β\alpha, \beta) are the roots of the equation (\mathrm{ax}^2+bx+c=\mathrm{bx}+\mathrm{c}=0), then the roots of the equation (\mathrm{ax}^2+bx(x+\mathrm{bx}(\mathrm{x}+1)+c(x+\mathrm{c}(\mathrm{x}+1)^2=0) are

Options

  1. A(\alpha-1, \beta-1)
  2. B(\alpha+1, \beta+1)
  3. C(αα−1,ββ−1\frac{\alpha}{\alpha-1}, \frac{\beta}{\beta-1})
  4. D(α1−α,β1−β\frac{\alpha}{1-\alpha}, \frac{\beta}{1-\beta})

Correct answer

D. (α1−α,β1−β\frac{\alpha}{1-\alpha}, \frac{\beta}{1-\beta})

Step-by-step solution

The second equation can be rewritten as (a\left(\frac{x}{x+1}\right)^2+b(xx+1)+\left(\frac{x}{x+1}\right)+c=0) and hence its roots correspond to (xx+1=α\frac{\mathrm{x}}{\mathrm{x}+1}=\alpha and (xx+1=β\frac{x}{x+1}=\beta. Hence (x=α1−α\frac{\alpha}{1-\alpha} and (β1−β\frac{\beta}{1-\beta}.
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